It looks like this is a known issue when connecting a Bluetooth device that has a microphone. A fix was very recently merged in libgnome-volume-control, as well as some work in pipewire. I’m not sure when this fix will be released and make its way to a Fedora update.
There’s a workaround to bypass the issue for now on that libgnome-volume-control thread from pv:
Workarounds are
wpctl settings bluetooth.autoswitch-to-headset-profile falseor downgrading wireplumber back to 0.5.12.
This thread seems useful for downgrading wireplummer on Fedora if you want to go that route. (Similar thread for silverblue).